Student (Print)
Section
Last, First Middle
Student (Sign)
Student ID
Instructor
MATH 152,
Fall 2007
Common Exam 1
Test Form A
Instructions:
You may not use notes, books, calculator or computer.
For Dept use Only:
1-10
/50
11
/10
12
/10
after 90 minutes and may not be returned.
13
/10
Part II is work out. Show all your work. Partial credit will be given.
14
/10
15
/10
Part I is multiple choice. There is no partial credit.
Mark the Scantron with a #2 pencil. For your own records,
also circle your choices in this exam. Scantrons will be collected
THE AGGIE CODE OF HONOR:
An Aggie does not lie, cheat or steal, or tolerate those who do.
TOTAL
1
Part I: Multiple Choice (5 points each)
There is no partial credit.
1. Compute
1
∫ 0 xe
x 2 +1
dx
a. 1 e
b.
c.
d.
e.
2
1 (e − 1)
2
1 e2
2
1 (e 2 − 1)
2
1 (e 2 − e)
2
2. Compute
π/2
∫0
x cos x dx
a. π − 1
2
b. 1 + π
c. π
2
2
d. 1 − π
e. π − 1
3. Find the area below the parabola, y = 3x − x 2 , above the x-axis.
a. 1
b.
c.
d.
e.
2
9
2
27
2
81
2
10
3
2
4. Find the average value of f(x) = e 3x on the interval [0, 2].
a. 1 (e 6 − 1)
b.
c.
d.
e.
5.
3
1 e6
3
1 (e 6 − 1)
6
1 e6
6
(e 6 − 1)
The region shown at the right is bounded
above by y = sin x and below by the x-axis.
It is rotated about the x-axis.
Find the volume swept out.
y
1.0
0.5
0.0
0
1
2
3
x
2
a. π
2
b. 2π 2
c. 2π
d. π
2
π
e.
4
6. The region in Problem 5 is rotated about the the line x = −1.
Which formula gives the volume swept out?
a.
b.
c.
d.
e.
π
∫ 0 π (1 + sin x) 2 − 1
π
∫ 0 2π(x + 1) sin x dx
π
∫ 0 π(x − 1) sin x dx
π
∫ −1 2πx sin x dx
π
∫ 0 π(1 + sin x) 2 dx
dx
3
7. The region bounded by the curves x = 1, y = 1 and y = 4
x
is rotated about the x-axis.
Find the volume swept out.
a.
b.
c.
d.
e.
8.
π(8 ln 4 − 15)
π(15 − 8 ln 4)
12π
9π
8π
A solid has a base which is a circle of radius 2
and has cross sections perpendicular to the y-axis
which are isosceles right triangles with a leg
on the base. Find the volume of the solid.
a. 32
b.
c.
d.
e.
3
64
3
128
3
16 π
3
32 π
3
4
9. A certain spring is at rest when its mass is at x = 0.
It requires 24 Joules of work to stretch it from x = 0 to x = 4 meters.
What is the force required to maintain the mass at 4 meters?
a.
b.
c.
d.
e.
48 Newtons
18 Newtons
12 Newtons
6 Newtons
24 Newtons
2
10. Find the partial fraction expansion for f(x) = 5x 3+ x + 12 .
x + 4x
a. 1 + 3x2 − 2
b.
c.
d.
e.
x
2
x
1
x
2
x
3
x
+
+
+
+
x +4
x−3
x2 + 4
2x + 3
x2 + 4
3x + 1
x2 + 4
2x + 1
x2 + 4
5
Part II: Work Out (10 points each)
Show all your work. Partial credit will be given.
11. Compute
a. (5 points)
∫ cos 3 θ dθ
b. (5 points)
∫ x 3 ln x dx
6
12. Find the area between the cubic y = x 3 − x 2 and the line y = 2x.
13.
A water tower is made by rotating the curve y = x 4 about the
y-axis, where x and y are in meters. If the tower is filled with water
(of density ρ = 1000 kg/m 3 ) up to height y = 25 m, how much
work is done to pump all the water out a faucet at height 30 m?
Assume the acceleration of gravity is g = 9. 8 m/sec 2 .
You may give your answer as a multiple of ρg.
7
1
x2
dx
(4 − x 2 ) 3/2
4
x − 4 dx
x 2 + 16
14. Compute
∫0
15. Compute
∫0
8